ZLB in two-country model

Dear @Max1,

I really hope you have the time to look at my problem :slight_smile: Any help is greatly appreciated!

I am trying to implement Occbin in a two-country DSGE model to analyse the international spillover effects of QE compared to conventional monetary policy at the ZLB. The model is from Alpanda and Kabaca (2020). The ZLB constraint is binding when r<pi/beta and the Taylor rule will in that case be replaced with r=pi/beta. All foreign economy variables are denoted with a β€œ_s” in the code.

In the model QE works by reducing the relative supply of long-term bonds outstanding, and for now I am only considering QE in the foreign economy. However, using Occbin whenever I try shocking to a variable related to bond supply or the foreign interest rate, the model does not converge.

Any suggestion as to why it isn’t working? I’m thinking I might be violating some equilibrium condition but I cannot figure out how to solve it.

The code is attached and I am thankful for any help or advice you can provide! I’m a novice at Dynare and have not used Occbin before.

QE_spillover_IRFS.mod (21.5 KB)

Best regards

No, unfortunately my time is very limited this month.

At a glance, I would say that you should use

[name='Foreign Taylor rule',bind = 'ZLB_s']
R_s = -log((pi_bar/betta));

name 'ZLB_s'; bind Rnot_s<-log((pi_bar/betta));

Thank you so much for your help @Max1! It is now running smoothly :slight_smile: When you have time, I hope you can answer a quick question: Is it possible to set up perfect foresight with occbin? It seems as if I cannot set a known path for an endogenous variable - and in my model I need to.

Best regards

Occbin assumes the presence of unexpected white noise shocks.

Basically, the solution algorithm resembles the extended path algorithm from Fair & Taylor (1983).

If you like to implement a perfect foresight simulation with occasionally binding constraints, you can do so by using the lmmcp option and mcp equation tags.

Thank you for the quick reply and your help! I will try to do so :slight_smile:

Best regards

Hi @Max1, I have a follow-up question: if the shock is a one-time unexpected at period 1 affecting the economy through AR process, then would the impulse response be the same in both Occbin and lmmcp?

No, because the solution method is different.
Occbin uses first order approx. of the different regimes and merges the different regimes via a sequence of guess and verify steps. Therefore, Occbin offers a piecewise-linear solution.
The perfect foresight solver uses a non-linear solution.